Adding Fractions with Unlike Denominators - Worksheet Digital - Free Printable

To solve the problem of adding unlike fractions, we need to follow these steps:

1. Find a Common Denominator: The denominators of the fractions must be made the same so that they can be added directly.
2. Adjust the Numerators: Once the common denominator is found, adjust the numerators of the fractions accordingly.
3. Add the Fractions: Add the adjusted numerators and keep the common denominator.
4. Simplify the Result: If possible, simplify the resulting fraction.

Let's solve each problem step by step.

---

Problem 1: \( \frac{1}{2} + \frac{1}{3} \)

- Step 1: Find the Least Common Denominator (LCD)
The denominators are 2 and 3. The LCD is 6.

- Step 2: Adjust the Fractions
\[
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
\]
\[
\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}
\]

- Step 3: Add the Fractions
\[
\frac{3}{6} + \frac{2}{6} = \frac{3 + 2}{6} = \frac{5}{6}
\]

- Step 4: Simplify
The fraction \(\frac{5}{6}\) is already in its simplest form.

Answer: \( \frac{5}{6} \)

---

Problem 2: \( \frac{1}{3} + \frac{3}{5} \)

- Step 1: Find the LCD
The denominators are 3 and 5. The LCD is 15.

- Step 2: Adjust the Fractions
\[
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
\]
\[
\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}
\]

- Step 3: Add the Fractions
\[
\frac{5}{15} + \frac{9}{15} = \frac{5 + 9}{15} = \frac{14}{15}
\]

- Step 4: Simplify
The fraction \(\frac{14}{15}\) is already in its simplest form.

Answer: \( \frac{14}{15} \)

---

Problem 3: \( \frac{1}{2} + \frac{2}{3} \)

- Step 1: Find the LCD
The denominators are 2 and 3. The LCD is 6.

- Step 2: Adjust the Fractions
\[
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
\]
\[
\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
\]

- Step 3: Add the Fractions
\[
\frac{3}{6} + \frac{4}{6} = \frac{3 + 4}{6} = \frac{7}{6}
\]

- Step 4: Simplify
The fraction \(\frac{7}{6}\) is already in its simplest form.

Answer: \( \frac{7}{6} \)

---

Problem 4: \( \frac{2}{5} + \frac{5}{6} \)

- Step 1: Find the LCD
The denominators are 5 and 6. The LCD is 30.

- Step 2: Adjust the Fractions
\[
\frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30}
\]
\[
\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}
\]

- Step 3: Add the Fractions
\[
\frac{12}{30} + \frac{25}{30} = \frac{12 + 25}{30} = \frac{37}{30}
\]

- Step 4: Simplify
The fraction \(\frac{37}{30}\) is already in its simplest form.

Answer: \( \frac{37}{30} \)

---

Problem 5: \( \frac{5}{6} + \frac{2}{5} \)

- Step 1: Find the LCD
The denominators are 6 and 5. The LCD is 30.

- Step 2: Adjust the Fractions
\[
\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}
\]
\[
\frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30}
\]

- Step 3: Add the Fractions
\[
\frac{25}{30} + \frac{12}{30} = \frac{25 + 12}{30} = \frac{37}{30}
\]

- Step 4: Simplify
The fraction \(\frac{37}{30}\) is already in its simplest form.

Answer: \( \frac{37}{30} \)

---

Problem 6: \( \frac{1}{4} + \frac{1}{6} \)

- Step 1: Find the LCD
The denominators are 4 and 6. The LCD is 12.

- Step 2: Adjust the Fractions
\[
\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}
\]
\[
\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}
\]

- Step 3: Add the Fractions
\[
\frac{3}{12} + \frac{2}{12} = \frac{3 + 2}{12} = \frac{5}{12}
\]

- Step 4: Simplify
The fraction \(\frac{5}{12}\) is already in its simplest form.

Answer: \( \frac{5}{12} \)

---

Problem 7: \( \frac{3}{7} + \frac{3}{5} \)

- Step 1: Find the LCD
The denominators are 7 and 5. The LCD is 35.

- Step 2: Adjust the Fractions
\[
\frac{3}{7} = \frac{3 \times 5}{7 \times 5} = \frac{15}{35}
\]
\[
\frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35}
\]

- Step 3: Add the Fractions
\[
\frac{15}{35} + \frac{21}{35} = \frac{15 + 21}{35} = \frac{36}{35}
\]

- Step 4: Simplify
The fraction \(\frac{36}{35}\) is already in its simplest form.

Answer: \( \frac{36}{35} \)

---

Problem 8: \( \frac{2}{5} + \frac{5}{9} \)

- Step 1: Find the LCD
The denominators are 5 and 9. The LCD is 45.

- Step 2: Adjust the Fractions
\[
\frac{2}{5} = \frac{2 \times 9}{5 \times 9} = \frac{18}{45}
\]
\[
\frac{5}{9} = \frac{5 \times 5}{9 \times 5} = \frac{25}{45}
\]

- Step 3: Add the Fractions
\[
\frac{18}{45} + \frac{25}{45} = \frac{18 + 25}{45} = \frac{43}{45}
\]

- Step 4: Simplify
The fraction \(\frac{43}{45}\) is already in its simplest form.

Answer: \( \frac{43}{45} \)

---

Problem 9: \( \frac{5}{8} + \frac{1}{2} \)

- Step 1: Find the LCD
The denominators are 8 and 2. The LCD is 8.

- Step 2: Adjust the Fractions
\[
\frac{5}{8} = \frac{5}{8}
\]
\[
\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}
\]

- Step 3: Add the Fractions
\[
\frac{5}{8} + \frac{4}{8} = \frac{5 + 4}{8} = \frac{9}{8}
\]

- Step 4: Simplify
The fraction \(\frac{9}{8}\) is already in its simplest form.

Answer: \( \frac{9}{8} \)

---

Problem 10: \( \frac{1}{6} + \frac{3}{4} \)

- Step 1: Find the LCD
The denominators are 6 and 4. The LCD is 12.

- Step 2: Adjust the Fractions
\[
\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}
\]
\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
\]

- Step 3: Add the Fractions
\[
\frac{2}{12} + \frac{9}{12} = \frac{2 + 9}{12} = \frac{11}{12}
\]

- Step 4: Simplify
The fraction \(\frac{11}{12}\) is already in its simplest form.

Answer: \( \frac{11}{12} \)

---

Final Answers:

\[
\boxed{
\begin{array}{cc}
\frac{1}{2} + \frac{1}{3} = \frac{5}{6} & \frac{1}{3} + \frac{3}{5} = \frac{14}{15} \\
\frac{1}{2} + \frac{2}{3} = \frac{7}{6} & \frac{2}{5} + \frac{5}{6} = \frac{37}{30} \\
\frac{5}{6} + \frac{2}{5} = \frac{37}{30} & \frac{1}{4} + \frac{1}{6} = \frac{5}{12} \\
\frac{3}{7} + \frac{3}{5} = \frac{36}{35} & \frac{2}{5} + \frac{5}{9} = \frac{43}{45} \\
\frac{5}{8} + \frac{1}{2} = \frac{9}{8} & \frac{1}{6} + \frac{3}{4} = \frac{11}{12}
\end{array}
}
\]